When you mow clover you stress it. One stress and perennial clover will recover well. If it has multiple stresses, it will be hurt at least. The Durana I plant is low growing and drought tolerant. I can mow it to 6" once established with no ill effects. For ladino which is not as drought tolerant, I'll mow 6" to 8" depending on conditions. If we have had plenty of rain or if I have a high probably of significant rain in the near term forecast, I'll mow it to 6" otherwise I'll mow it to 8".
I won't speak to all clover since some other clovers are much taller growing than Ladino or Durana. But for them, in your case it will really depend on conditions. One technique I use for clover depends heavily on good timing. I will suppress established clover either with 1 qt/ac gly (if old and weedy) or by mowing it flat with a bushhog set so low it almost scalps. I then drill radish and cereal into the clover. I do this in the fall as nights are just getting cooler with a soaking rain in the forecast. The cereal and radish germinate quickly and get above the clover before it bounces back
As you can see, if conditions are right, established clover can bounce back very quickly. However, if you get a drought after mowing low, multiple simultaneous stresses can hurt the clover.
Thanks,
Jack